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Chen's theorem (776 words) [view diff] no match in snippet view article find links to article

In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes, or a prime and a semiprime

Riemann–von Mangoldt formula (415 words) [view diff] no match in snippet view article find links to article

In mathematics, the Riemann–von Mangoldt formula, named for Bernhard Riemann and Hans Carl Friedrich von Mangoldt, describes the distribution of the zeros

Riemann–Siegel formula (853 words) [view diff] case mismatch in snippet view article find links to article

dx} Barkan, Eric; Sklar, David (2018). "On Riemanns Nachlass for Analytic Number Theory: A translation of Siegel's Uber". arXiv:1810.05198 [math.HO]. Berry

Kronecker limit formula (536 words) [view diff] exact match in snippet view article find links to article

function Serge Lang, Elliptic functions, ISBN 0-387-96508-4 C. L. Siegel, Lectures on advanced analytic number theory, Tata institute 1961. Chapter0.pdf

Hardy–Ramanujan theorem (628 words) [view diff] exact match in snippet view article find links to article

Analytic number theory

Barban–Davenport–Halberstam theorem (348 words) [view diff] no match in snippet view article find links to article

In mathematics, the Barban–Davenport–Halberstam theorem is a statement about the distribution of prime numbers in an arithmetic progression. It is known

List of lemmas (525 words) [view diff] no match in snippet view article find links to article

This following is a list of lemmas (or, "lemmata", i.e. minor theorems, or sometimes intermediate technical results factored out of proofs). See also list

Maier's theorem (364 words) [view diff] no match in snippet view article find links to article

In number theory, Maier's theorem is a theorem due to Helmut Maier about the numbers of primes in short intervals for which Cramér's probabilistic model

Jurkat–Richert theorem (631 words) [view diff] no match in snippet view article find links to article

The Jurkat–Richert theorem is a mathematical theorem in sieve theory. It is a key ingredient in proofs of Chen's theorem on Goldbach's conjecture.: 272

Chebyshev's bias (1,040 words) [view diff] no match in snippet view article find links to article

In number theory, Chebyshev's bias is the phenomenon that most of the time, there are more primes of the form 4k + 3 than of the form 4k + 1, up to the

Fundamental lemma of sieve theory (961 words) [view diff] no match in snippet view article find links to article

In number theory, the fundamental lemma of sieve theory is any of several results that systematize the process of applying sieve methods to particular

Borwein's algorithm (1,545 words) [view diff] case mismatch in snippet view article find links to article

algorithms can be found in the book Pi and the AGM – A Study in Analytic Number Theory and Computational Complexity. These two are examples of a Ramanujan–Sato

Landsberg–Schaar relation (381 words) [view diff] no match in snippet view article find links to article

In number theory and harmonic analysis, the Landsberg–Schaar relation (or identity) is the following equation, which is valid for arbitrary positive integers

List of Jewish American mathematicians (700 words) [view diff] exact match in snippet view article find links to article

number theory and algebraic geometry Peter Sarnak (born 1953), analytic number theory; Pólya Prize (1998), Cole Prize (2005), Wolf Prize (2014) Yakov

Dirichlet L-function (1,629 words) [view diff] exact match in snippet view article find links to article

Montgomery, Hugh L. (1994). Ten lectures on the interface between analytic number theory and harmonic analysis. Regional Conference Series in Mathematics

Friedrich Karl Schmidt (439 words) [view diff] exact match in snippet view article find links to article

quadratic fields). Several years later F. K. Schmidt treated general analytic number theory including the functional equation of the zeta function for function

Harmonic mean (5,958 words) [view diff] no match in snippet view article find links to article

In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is the most appropriate average for ratios and rates such as speeds

Ramanujan's master theorem (4,751 words) [view diff] no match in snippet view article find links to article

In mathematics, Ramanujan's master theorem, named after Srinivasa Ramanujan, is a technique that provides an analytic expression for the Mellin transform

Dirichlet convolution (2,587 words) [view diff] case mismatch in snippet view article find links to article

found in this article. Schmidt, Maxie. Apostol's Introduction to Analytic Number Theory. This identity is a little special something I call "croutons".

Divisor summatory function (1,936 words) [view diff] exact match in snippet view article find links to article

Montgomery, Hugh L. (1994). Ten lectures on the interface between analytic number theory and harmonic analysis. Regional Conference Series in Mathematics

Gauss sum (918 words) [view diff] exact match in snippet view article find links to article

Mathematics, 97, (2006). Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Paul T. Bateman (619 words) [view diff] case mismatch in snippet view article find links to article

Mathematical Reviews Committee for 5 years. Bateman was a coauthor of Analytic Number Theory: An Introductory Course. He was also a contributor to the second

Deshouillers–Dress–Tenenbaum theorem (1,099 words) [view diff] no match in snippet view article find links to article

The Deshouillers–Dress–Tenenbaum theorem (or in short DDT theorem) is a result from probabilistic number theory, which describes the probability distribution

Alex Kontorovich (455 words) [view diff] exact match in snippet view article find links to article

Kontorovich is an American mathematician who works in the areas of analytic number theory, automorphic forms and representation theory, L-functions, harmonic

Carlos J. Moreno (164 words) [view diff] exact match in snippet view article find links to article

Cambridge University Press. 1991. ISBN 9780521342520. Advanced analytic number theory: L-functions. Mathematical Surveys. Vol. 115. Americal Mathematical

Arithmetic number (302 words) [view diff] exact match in snippet view article find links to article

arithmetic mean of the divisors of an integer". In Knopp, M.I. (ed.). Analytic number theory, Proc. Conf., Temple Univ., 1980 (PDF). Lecture Notes in Mathematics

Von Staudt–Clausen theorem (928 words) [view diff] case mismatch in snippet view article find links to article

congruence H. Rademacher, Analytic Number Theory, Springer-Verlag, New York, 1973. T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976

Matsumoto zeta function (95 words) [view diff] exact match in snippet view article find links to article

Matsumoto, Kohji (1990), "Value-distribution of zeta-functions", Analytic number theory ({T}okyo, 1988), Lecture Notes in Math., vol. 1434, Berlin, New

Emil Grosswald (1,359 words) [view diff] case mismatch in snippet view article find links to article

edited for publication Rademacher's posthumous textbook Topics in Analytic Number Theory. He published numerous other books and countless articles. Grosswald

Selberg class (1,908 words) [view diff] case mismatch in snippet view article find links to article

class of Dirichlet series", Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), Salerno: Univ. Salerno, pp. 367–385, MR 1220477

Schnirelmann density (2,576 words) [view diff] case mismatch in snippet view article find links to article

Linnik, Yu. V. (1966). L.J. Mordell (ed.). Elementary Methods in Analytic Number Theory. George Allen & Unwin. Mann, Henry B. (1976). Addition Theorems:

Strassmann's theorem (213 words) [view diff] case mismatch in snippet view article find links to article

exponential function Murty, M. Ram (2002). Introduction to P-Adic Analytic Number Theory. American Mathematical Society. p. 35. ISBN 978-0-8218-3262-2. Straßmann

Manin conjecture (371 words) [view diff] exact match in snippet view article find links to article

Manin's conjecture for del Pezzo surfaces". In Duke, William (ed.). Analytic number theory. A tribute to Gauss and Dirichlet. Proceedings of the Gauss-Dirichlet

Stanisław Łojasiewicz (135 words) [view diff] exact match in snippet view article find links to article

at Austin Poland / Canada / United States Recent developments in analytic number theory 2024 László Lovász Eötvös Loránd University Hungary The infinite

Euler function (789 words) [view diff] exact match in snippet view article find links to article

Sequences. OEIS Foundation. Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Graduate Texts in Mathematics (5,056 words) [view diff] case mismatch in snippet view article find links to article

Manifolds, John M. Lee (2018, 2nd ed., ISBN 978-3-319-91754-2) Analytic Number Theory , Donald J. Newman (1998, ISBN 978-0-387-98308-0) Nonsmooth Analysis

Graduate Studies in Mathematics (4,546 words) [view diff] case mismatch in snippet view article find links to article

Geometric Optics, Jeffrey Rauch (2012, ISBN 978-0-8218-7291-8) 134 Analytic Number Theory: Exploring the Anatomy of Integers, Jean-Marie De Koninck, Florian

Arithmetic–geometric mean (3,029 words) [view diff] case mismatch in snippet view article find links to article

Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (First ed.). Wiley-Interscience. ISBN 0-471-83138-7

Isaac Jacob Schoenberg (509 words) [view diff] exact match in snippet view article find links to article

the Universities of Berlin and Göttingen, working on a topic in analytic number theory suggested by Issai Schur. He presented his thesis to the University

Sumset (370 words) [view diff] exact match in snippet view article find links to article

Bruce C.; Diamond, Harold G.; Halberstam, Heini; et al. (eds.). Analytic number theory. Proceedings of a conference in honor of Paul T. Bateman, held on

Malta Mathematical Society (832 words) [view diff] case mismatch in snippet view article find links to article

Differential Geometry, six lectures by Prof. Joseph Muscat (Summer, 2021) Analytic Number Theory and its Applications, three lectures by Luke Collins (Summer, 2022)

Wiener–Ikehara theorem (413 words) [view diff] case mismatch in snippet view article find links to article

0226.02, JSTOR 1968102 K. Chandrasekharan (1969). Introduction to Analytic Number Theory. Grundlehren der mathematischen Wissenschaften. Springer-Verlag

Peter D. T. A. Elliott (164 words) [view diff] case mismatch in snippet view article find links to article

and Integer Products, Springer-Verlag New York, 1985 Duality in Analytic Number Theory, Cambridge University Press, 1997 Analytic and Elementary Number

Genus character (151 words) [view diff] case mismatch in snippet view article find links to article

of the genus field of K). Chapter II of Siegel, Carl, Advanced Analytic Number Theory Bertolini, Massimo; Darmon, Henri (2009), "The rationality of Stark-Heegner

Virasena (539 words) [view diff] case mismatch in snippet view article find links to article

e.g., Shparlinski, Igor (2013), Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness, Progress in Computer

Completely multiplicative function (1,008 words) [view diff] case mismatch in snippet view article find links to article

series Multiplicative function Apostol, Tom (1976). Introduction to Analytic Number Theory. Springer. pp. 30. ISBN 0-387-90163-9. Apostol, p. 36 Apostol pg

9000 (number) (987 words) [view diff] case mismatch in snippet view article

from the Institute of Mathematical Analysis (in, New Aspects of Analytic Number Theory)]. 1639. Kyoto: RIMS: 69–79. hdl:2433/140555. S2CID 38654417. Sloane

Chebyshev function (2,341 words) [view diff] case mismatch in snippet view article find links to article

1016/j.eswa.2017.09.051. Apostol, Tom M. (2010). Introduction to Analytic Number Theory. Springer. pp. 75–76. Rosser, J. Barkley; Schoenfeld, Lowell (1962)

Bring radical (8,570 words) [view diff] case mismatch in snippet view article find links to article

Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (First ed.). Wiley-Interscience. ISBN 0-471-83138-7

Fabry gap theorem (266 words) [view diff] exact match in snippet view article find links to article

Montgomery, Hugh L. (1994). Ten lectures on the interface between analytic number theory and harmonic analysis. Regional Conference Series in Mathematics

Andrew Guinand (466 words) [view diff] case mismatch in snippet view article find links to article

1017/s0013091500025001. ISSN 1464-3839. Richard E. Bellman (1980), Analytic Number Theory An Introduction, The Benjamin/ Cummings Publishing Company, Inc

Victor Moll (801 words) [view diff] case mismatch in snippet view article find links to article

Project Vardi, Ilan (April 1988). "Integrals: An Introduction to Analytic Number Theory" (PDF). American Mathematical Monthly. 95 (4): 308–315. doi:10.2307/2323562

Yuri Linnik (463 words) [view diff] exact match in snippet view article find links to article

Stalin and Lenin Prizes. He died in Leningrad. Linnik's theorem in analytic number theory The dispersion method (which allowed him to solve the Titchmarsh

On-Line Encyclopedia of Integer Sequences (5,601 words) [view diff] case mismatch in snippet view article find links to article

Publications, 1965, pp. 805-811. T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1986, p. 48. LINKS Reinhard Zumkeller, Table of

Jordan's totient function (921 words) [view diff] case mismatch in snippet view article find links to article

ISBN 0-8284-0086-5. JFM 47.0100.04. M. Ram Murty (2001). Problems in Analytic Number Theory. Graduate Texts in Mathematics. Vol. 206. Springer-Verlag. p. 11

Selberg's identity (431 words) [view diff] case mismatch in snippet view article find links to article

book (see also this link). Apostol, T. (1976). Introduction to Analytic Number Theory. New York: Springer. p. 46 (Section 2.19). ISBN 0-387-90163-9. Pisot

Elliptic integral (7,832 words) [view diff] case mismatch in snippet view article find links to article

Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (First ed.). Wiley-Interscience. ISBN 0-471-83138-7

Centered square number (805 words) [view diff] exact match in snippet view article find links to article

JSTOR 2688938, MR 1571197. Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Harold Davenport (956 words) [view diff] exact match in snippet view article find links to article

Association of America. Stark, H. M. (1971). "Review: Introduction to analytic number theory, by K. Chandrasekharan; Arithmetical functions, by K. Chandrasekharan;

Additive function (1,291 words) [view diff] exact match in snippet view article find links to article

of arithmetical functions), (Obzornik mat, fiz. 49 (2002) 4, pp. 97–108) (MSC (2000) 11A25) Iwaniec and Kowalski, Analytic number theory, AMS (2004).

Mei-Chu Chang (344 words) [view diff] exact match in snippet view article find links to article

citation reads "For contributions to arithmetic combinatorics, analytic number theory, and algebraic geometry." In 2009 she was chosen to give a plenary

Modular lambda function (3,503 words) [view diff] case mismatch in snippet view article find links to article

Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (First ed.). Wiley-Interscience. ISBN 0-471-83138-7

Alexandru Zaharescu (325 words) [view diff] exact match in snippet view article find links to article

the American Mathematical Society in 2017, for contributions to analytic number theory. A conference in honor of his 60th birthday was held in June 2021

Donald J. Newman (710 words) [view diff] exact match in snippet view article find links to article

problem seminar. New York: Springer. ISBN 0-387-90765-3. --. (1998) Analytic number theory. New York: Springer. ISBN 0-387-98308-2 (#177 in the Graduate Texts

Polignac's conjecture (898 words) [view diff] case mismatch in snippet view article find links to article

Retrieved 2014-02-21. Bateman, Paul T.; Diamond, Harold G. (2004), Analytic Number Theory, World Scientific, p. 313, ISBN 981-256-080-7, Zbl 1074.11001. Alphonse

73 (number) (2,004 words) [view diff] case mismatch in snippet view article

[Notes from the Institute of Mathematical Analysis] (New Aspects of Analytic Number Theory). 1639. Kyoto: RIMS: 69–79. hdl:2433/140555. S2CID 38654417. Gary

P-adic valuation (1,380 words) [view diff] exact match in snippet view article find links to article

Publishers. p. 9.[ISBN missing] Murty, M. Ram (2001). Problems in analytic number theory. Graduate Texts in Mathematics. Vol. 206. Springer-Verlag, New York

Steven Gaal (729 words) [view diff] exact match in snippet view article find links to article

sequence periodic?" Gaal, Steven A. (1961). Lectures on algebraic and analytic number theory: With special emphasis on the theory of the Zeta functions of number

Well-ordering principle (1,184 words) [view diff] case mismatch in snippet view article find links to article

for all positive integers. Apostol, Tom (1976). Introduction to Analytic Number Theory. New York: Springer-Verlag. pp. 13. ISBN 0-387-90163-9. Lovász,

Polymath Project (1,556 words) [view diff] exact match in snippet view article find links to article

Chowla and Elliott conjectures, making use of recent advances in analytic number theory concerning correlations of values of multiplicative functions. The

Von Mangoldt function (1,839 words) [view diff] exact match in snippet view article find links to article

ISBN 978-0-8218-4970-5, MR 2647984 Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Richard S. Varga (556 words) [view diff] no match in snippet view article find links to article

particularly Padé approximation (often with Edward B. Saff, Jr.)—and analytic number theory, including high-precision calculations related to the Riemann hypothesis

Bell series (713 words) [view diff] exact match in snippet view article find links to article

{1-2x^{k}+x^{k+1}}{1-x}}.} Bell numbers Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Class number problem (1,235 words) [view diff] case mismatch in snippet view article find links to article

Class-Number Problems". In Duke, William; Tschinkel, Yuri (eds.). Analytic Number Theory: A Tribute to Gauss and Dirichlet (pdf). Clay Mathematics Proceedings

Infosys Prize (2,078 words) [view diff] exact match in snippet view article find links to article

Soundararajan Stanford University Awarded "for his path breaking work in analytic number theory and development of new techniques to study critical values of general

Green–Tao theorem (1,538 words) [view diff] exact match in snippet view article find links to article

progressions of primes". In Duke, William; Tschinkel, Yuri (eds.). Analytic number theory. Clay Mathematics Proceeding. Vol. 7. Providence, RI: American Mathematical

William Duke (mathematician) (562 words) [view diff] exact match in snippet view article

the American Mathematical Society in 2016 "for contributions to analytic number theory and the theory of automorphic forms". Duke is an Editorial Board

Duffin–Schaeffer theorem (706 words) [view diff] exact match in snippet view article find links to article

Montgomery, Hugh L. (1994). Ten lectures on the interface between analytic number theory and harmonic analysis. Regional Conference Series in Mathematics

Florian Luca (355 words) [view diff] case mismatch in snippet view article find links to article

Mathematical Society 42 (3), 478-488, 2010 with Jean-Marie De Koninck: Analytic Number Theory: Exploring the Anatomy of Integers, American Mathematical Society

Marvin Knopp (541 words) [view diff] case mismatch in snippet view article find links to article

theory of modular forms. Knopp, Marvin (1970). Modular Functions in Analytic Number Theory. Rand McNally. ISBN 0-528-60000-1. Knopp, Marvin; Berndt, Bruce

Isaak Moiseevich Milin (1,092 words) [view diff] case mismatch in snippet view article find links to article

conjecture about logarithmic coefficients of univalent functions., In: Analytic Number Theory and Function Theory, v.5, Zapiski Nauchn. Seminarov LOMI, 125, 1983

Twin prime (2,734 words) [view diff] case mismatch in snippet view article find links to article

ISSN 0365-4524. JFM 45.0330.16. Bateman, Paul T.; Diamond, Harold G. (2004). Analytic Number Theory. World Scientific. pp. 313 and 334–335. ISBN 981-256-080-7. Zbl 1074

Character group (1,515 words) [view diff] exact match in snippet view article find links to article

OCLC 54475368. See chapter 6 of Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Landau's problems (2,106 words) [view diff] case mismatch in snippet view article find links to article

the Goldbach conjecture. Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989). Università di Salerno. pp. 115–155. Yu V Linnik

List of Jewish mathematicians (15,830 words) [view diff] exact match in snippet view article find links to article

partial differential equations Theodor Estermann (1902–1991), analytic number theory: 260 Gino Fano (1871–1952), mathematician Yehuda Farissol (15th

Miguel Walsh (595 words) [view diff] exact match in snippet view article find links to article

of the Salem Prize, given "for contributions to ergodic theory, analytic number theory, and the development of the polynomial method, including a convergence

Jacobi triple product (1,266 words) [view diff] exact match in snippet view article find links to article

Chapter 14, theorem 14.6 of Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Yuri Tschinkel (555 words) [view diff] case mismatch in snippet view article find links to article

new perspectives", Birkhäuser 2009 as editor with William Duke: Analytic Number Theory – a tribute to Gauss and Dirichlet , American Mathematical Society

Bôcher Memorial Prize (2,146 words) [view diff] exact match in snippet view article find links to article

applications of these tools in harmonic analysis, incidence geometry, analytic number theory, and partial differential equations" including: A restriction estimate

Cayley's nodal cubic surface (447 words) [view diff] case mismatch in snippet view article find links to article

points on Cayley's cubic surface", Proceedings of the Session in Analytic Number Theory and Diophantine Equations, Bonner Math. Schriften, vol. 360, Bonn:

Baum–Sweet sequence (994 words) [view diff] case mismatch in snippet view article find links to article

W.T. Gowers; H. Halbertstam; W.M. Schmidt; R.C. Vaughan (eds.). Analytic Number Theory: Essays in Honour of Klaus Roth (PDF). Cambridge University Press

Sicherman dice (1,083 words) [view diff] case mismatch in snippet view article find links to article

doi:10.1038/scientificamerican0278-19 Newman, Donald J. (1998). Analytic Number Theory. Springer-Verlag. ISBN 0-387-98308-2. Two-cube calendar Mathworld's

List of alumni of Trinity College, Cambridge (3,861 words) [view diff] exact match in snippet view article find links to article

H. Hardy (1877–1947), mathematician; A Mathematician's Apology, analytic number theory, Savilian Professor of Geometry in Oxford Sir James Jeans (1877–1946)

Zeta function regularization (2,125 words) [view diff] exact match in snippet view article find links to article

formula – Formula to calculate the sum of an arithmetic function in analytic number theory Renormalization – Method in physics used to deal with infinities

Möbius inversion formula (2,609 words) [view diff] exact match in snippet view article find links to article

Goldman 1975, pp. 789–803 Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Shapiro polynomials (948 words) [view diff] exact match in snippet view article find links to article

Bruce C.; Diamond, Harold G.; Halberstam, Heini; et al. (eds.). Analytic number theory. Proceedings of a conference in honor of Paul T. Bateman, held on

Szemerédi's theorem (2,490 words) [view diff] exact match in snippet view article find links to article

New bounds for Szemeredi's theorem, II: A new bound for r_4(N). Analytic number theory. Essays in honour of Klaus Roth on the occasion of his 80th birthday

Robert D. Hough (249 words) [view diff] exact match in snippet view article find links to article

America. Montgomery, Hugh (1994). Ten lectures on the interface of analytic number theory and harmonic analysis. American Mathematical Society. ISBN 978-0821807378

Vojtěch Jarník (2,201 words) [view diff] case mismatch in snippet view article find links to article

Gorodnik, Alexander; Peyerimhoff, Norbert (eds.), Dynamics and Analytic Number Theory: Proceedings of the Durham Easter School 2014, London Mathematical

James Cogdell (988 words) [view diff] exact match in snippet view article find links to article

automorphic forms (within the context of the Langlands program), and analytic number theory. In collaboration with Piatetski-Shapiro, he proved converse theorems

Erdős–Fuchs theorem (1,728 words) [view diff] exact match in snippet view article find links to article

278–284. doi:10.1090/S0002-9939-1963-0144876-1. Newman, D. J. (1998). Analytic number theory. GTM. Vol. 177. New York: Springer. pp. 31–38. ISBN 0-387-98308-2

Multiplication theorem (1,968 words) [view diff] exact match in snippet view article find links to article

"Legendre Duplication Formula". MathWorld. Apostol, Introduction to analytic number theory, Springer Milton Abramowitz and Irene A. Stegun, eds. Handbook of

Quadratic Gauss sum (1,660 words) [view diff] exact match in snippet view article find links to article

Wiley and Sons. ISBN 0-471-12807-4. Iwaniec, Henryk; Kowalski, Emmanuel (2004). Analytic number theory. American Mathematical Society. ISBN 0-8218-3633-1.

ATS theorem (1,798 words) [view diff] exact match in snippet view article find links to article

Montgomery, Hugh (1994). Ten lectures on the interface between analytic number theory and harmonic analysis. Providence, R.I: Published for the Conference

Arithmetic function (7,555 words) [view diff] case mismatch in snippet view article find links to article

Functions ..., ch. 6 eq. 3 Tom M. Apostol (1976), Introduction to Analytic Number Theory, Springer Undergraduate Texts in Mathematics, ISBN 0-387-90163-9

Multiplicative function (3,626 words) [view diff] exact match in snippet view article find links to article

series See chapter 2 of Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Pi (17,250 words) [view diff] case mismatch in snippet view article find links to article

Borwein, Jonathan; Borwein, Peter (1987). Pi and the AGM: a Study in Analytic Number Theory and Computational Complexity. Wiley. ISBN 978-0-471-31515-5. Bailey

Pentagonal number theorem (2,118 words) [view diff] exact match in snippet view article find links to article

Série A. 92: 448–450. Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Alexei Venkov (691 words) [view diff] exact match in snippet view article find links to article

automorphic functions, the Selberg zeta-function, and some problems of analytic number theory and mathematical physics, Russian Mathematical Surveys, vol. 34

Bertram Martin Wilson (1,361 words) [view diff] case mismatch in snippet view article find links to article

and B. M. Wilson, Chapter 5 of Ramanujan's second notebook, in Analytic Number Theory, Lecture Notes in Mathematics No. 899, M. I. Knopp, ed., Springer-Verlag

Minkowski's theorem (2,350 words) [view diff] case mismatch in snippet view article find links to article

Schoißengeier, Johannes; Taschner, Rudolf (2012) [1991]. Geometric and Analytic Number Theory. Springer. ISBN 978-3-642-75306-0. Lekkerkerker, C.G. (2014) [1969]

Normal number (4,302 words) [view diff] exact match in snippet view article find links to article

JSTOR 2695618, Zbl 1036.11035 Murty, Maruti Ram (2007), Problems in analytic number theory (2 ed.), Springer, ISBN 978-0-387-72349-5 Nakai, Y.; Shiokawa, I

Natural logarithm (5,882 words) [view diff] case mismatch in snippet view article find links to article

Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (First ed.). Wiley-Interscience. ISBN 0-471-83138-7

Undergraduate Texts in Mathematics (4,190 words) [view diff] case mismatch in snippet view article find links to article

ISBN 978-0-387-90202-9. Apostol, Tom M. (1976). Introduction to Analytic Number Theory. ISBN 978-0-387-90163-3. Sigler, L. E. (1976). Algebra. ISBN 978-0-387-90195-4

Sidon sequence (2,208 words) [view diff] case mismatch in snippet view article find links to article

1016/0022-314x(91)90083-n. ISSN 0022-314X. Graham, S. W. (1996), "Bh sequences", Analytic Number Theory, Boston, MA: Birkhäuser Boston, pp. 431–449, ISBN 978-1-4612-8645-5

J-invariant (4,738 words) [view diff] case mismatch in snippet view article find links to article

Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (First ed.). Wiley-Interscience. ISBN 0-471-83138-7

IIT Tirupati (3,088 words) [view diff] case mismatch in snippet view article find links to article

of mathematics and statistics, including Representation Theory, Analytic Number Theory, Fractals, Fixed Point Theory, Partial Differential Equations, Numerical

1 + 2 + 3 + 4 + ⋯ (4,219 words) [view diff] case mismatch in snippet view article find links to article

475–476. ISBN 0-486-66165-2. Stopple, Jeffrey (2003). A Primer of Analytic Number Theory: From Pythagoras to Riemann. p. 202. ISBN 0-521-81309-3.. Knopp

Rudin–Shapiro sequence (2,732 words) [view diff] exact match in snippet view article find links to article

Bruce C.; Diamond, Harold G.; Halberstam, Heini; et al. (eds.). Analytic number theory. Proceedings of a conference in honor of Paul T. Bateman, held on

Bernoulli number (13,056 words) [view diff] case mismatch in snippet view article find links to article

37236/1876, S2CID 10467873 Arfken (1970), p. 463. Rademacher, H. (1973), Analytic Number Theory, New York City: Springer-Verlag. Boole, G. (1880), A treatise of

Quadratic integer (2,911 words) [view diff] case mismatch in snippet view article find links to article

81 P. Weinberger, On Euclidean rings of algebraic integers. In: Analytic Number Theory (St. Louis, 1972), Proc. Sympos. Pure Math. 24(1973), 321–332. Harper

Computational complexity of mathematical operations (1,576 words) [view diff] case mismatch in snippet view article find links to article

1137/0209036. Borwein, J.; Borwein, P. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity. Wiley. ISBN 978-0-471-83138-9. OCLC 755165897

Root of unity (5,944 words) [view diff] case mismatch in snippet view article find links to article

306. ISBN 0-8176-3743-5. Apostol, Tom M. (1976). Introduction to Analytic Number Theory. Undergraduate Texts in Mathematics. Springer. p. 160. doi:10

Naor–Reingold pseudorandom function (1,975 words) [view diff] case mismatch in snippet view article find links to article

S2CID 8665271. Shparlinski, Igor (2003), Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness (first ed.), Birkhäuser

Fibonacci sequence (13,066 words) [view diff] case mismatch in snippet view article find links to article

Jonathan M.; Borwein, Peter B. (July 1998), Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity, Wiley, pp. 91–101, ISBN 978-0-471-31515-5

Hurwitz zeta function (4,190 words) [view diff] exact match in snippet view article find links to article

MR 2723248. See chapter 12 of Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Bernoulli polynomials (4,328 words) [view diff] exact match in snippet view article find links to article

York. (See Chapter 23) Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

Abc conjecture (4,588 words) [view diff] case mismatch in snippet view article find links to article

problems". In Chen, W. W. L. (ed.). Proceedings of the Symposium on Analytic Number Theory. London: Imperial College. Mollin, R.A. (2009). "A note on the ABC-conjecture"

Logarithm (11,674 words) [view diff] exact match in snippet view article find links to article

ISBN 978-0-8218-4873-9, chapter 5 Bateman, P.T.; Diamond, Harold G. (2004), Analytic number theory: an introductory course, New Jersey: World Scientific, ISBN 978-981-256-080-3

Binary logarithm (5,128 words) [view diff] case mismatch in snippet view article find links to article

e.g., Shparlinski, Igor (2013), Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness, Progress in Computer

List of conjectures (1,461 words) [view diff] exact match in snippet view article find links to article

and Larry Guth Main conjecture in Vinogradov's mean-value theorem analytic number theory Bourgain–Demeter–Guth theorem, ⇐ decoupling theorem 2018 Karim Adiprasito

List of people educated at Fettes College (1,598 words) [view diff] exact match in snippet view article find links to article

ornithologist. Robert Alexander Rankin, mathematician who worked in analytic number theory. Cecil Reddie, educationalist. Arthur David Ritchie, chemical physiologist

Dirac delta function (14,230 words) [view diff] case mismatch in snippet view article find links to article

3. Milovanović, Gradimir V.; Rassias, Michael Th (2014-07-08). Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M

Lemniscate constant (5,923 words) [view diff] case mismatch in snippet view article find links to article

Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (First ed.). Wiley-Interscience. ISBN 0-471-83138-7

Divisibility rule (6,801 words) [view diff] exact match in snippet view article find links to article

84, March 2000, 79–81. Apostol, Tom M. (1976). Introduction to analytic number theory. Undergraduate Texts in Mathematics. Vol. 1. Springer-Verlag.

Method of steepest descent (5,062 words) [view diff] case mismatch in snippet view article find links to article

in Barkan, Eric; Sklar, David (2018), "On Riemanns Nachlass for Analytic Number Theory: A translation of Siegel's Uber", arXiv:1810.05198 [math.HO]. Poston

Generating function (14,462 words) [view diff] exact match in snippet view article find links to article

identity". Math Overflow. 2017. Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag

List of mathematical constants (3,567 words) [view diff] case mismatch in snippet view article find links to article

Perelli; C. Viola; D.R. Heath-Brown; H.Iwaniec; J. Kaczorowski (2002). Analytic Number Theory. Springer. p. 29. ISBN 978-3-540-36363-7. Richard E. Crandall (2012)

Polylogarithm (10,139 words) [view diff] case mismatch in snippet view article find links to article

MathWorld. Weisstein, Eric W. "Dilogarithm". MathWorld. Algorithms in Analytic Number Theory provides an arbitrary-precision, GMP-based, GPL-licensed implementation

List of formulae involving π (8,342 words) [view diff] case mismatch in snippet view article find links to article

Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity (First ed.). Wiley-Interscience. ISBN 0-471-83138-7

List of Stuyvesant High School people (6,950 words) [view diff] exact match in snippet view article find links to article

Sciences (Massachusetts Institute of Technology) D. J. Newman (1947) – analytic number theory, long-time editor of problems section in the American Mathematical

Carl Johan Malmsten (3,818 words) [view diff] exact match in snippet view article find links to article

S2CID 254982221. PDF Vardi, Ilan (1988). "Integrals, an introduction to analytic number theory". Amer. Math. Monthly. 95 (4): 308–315. doi:10.2307/2323562. ISSN 0002-9890

Ramanujan's sum (5,818 words) [view diff] case mismatch in snippet view article find links to article

MR 0568909. Zbl 0423.10001. Knopfmacher, John (1990) [1975]. Abstract Analytic Number Theory (2nd ed.). New York: Dover. ISBN 0-486-66344-2. Zbl 0743.11002.

Average order of an arithmetic function (4,093 words) [view diff] case mismatch in snippet view article find links to article

ISBN 0-521-41261-7. Zbl 0831.11001. Tom M. Apostol (1976), Introduction to Analytic Number Theory, Springer Undergraduate Texts in Mathematics, ISBN 0-387-90163-9

List of Indian inventions and discoveries (22,546 words) [view diff] case mismatch in snippet view article find links to article

e.g., Shparlinski, Igor (2013), Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness, Progress in Computer

History of logarithms (5,447 words) [view diff] case mismatch in snippet view article find links to article

e.g., Shparlinski, Igor (2013), Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness, Progress in Computer

Multiple zeta function (6,076 words) [view diff] case mismatch in snippet view article find links to article

and other multiple zeta-functions", Proceedings of the Session in Analytic Number Theory and Diophantine Equations, Bonner Math. Schriften, vol. 360, Bonn:

Glossary of artificial intelligence (29,481 words) [view diff] case mismatch in snippet view article find links to article

ISSN 2050-3318. Bachmann, Paul (1894). Analytische Zahlentheorie [Analytic Number Theory] (in German). Vol. 2. Leipzig: Teubner. Landau, Edmund (1909). Handbuch

Glossary of computer science (23,955 words) [view diff] case mismatch in snippet view article find links to article

ISSN 2050-3318. Bachmann, Paul (1894). Analytische Zahlentheorie [Analytic Number Theory] (in German). Vol. 2. Leipzig: Teubner. Landau, Edmund (1909). Handbuch

Gradshteyn and Ryzhik (11,967 words) [view diff] case mismatch in snippet view article find links to article

[22]) Vardi, Ilan (April 1988). "Integrals: An Introduction to Analytic Number Theory" (PDF). American Mathematical Monthly. 95 (4): 308–315. doi:10.2307/2323562

Chang Shih-Hsun (1,426 words) [view diff] exact match in snippet view article find links to article

integral equations, group theory, number theory, modern algebra, analytic number theory, algebraic number theory, variational calculus, complex variable

Absolutely and completely monotonic functions and sequences (1,420 words) [view diff] case mismatch in snippet view article find links to article

Completely Monotonic Functions (pp. 144 - 179). Milan Merkle (2014). Analytic Number Theory, Approximation Theory, and Special Functions. Springer. pp. 347–364